Question

Solve L(sin4t) ?

Answer 1

Guessing this is a Laplace transform request

Explanation:

`mathbb L {cos omega t color(red)(-) i sin omega t } = mathbb L {e^(-i omega t) }`

`= int_0^(oo) e^(-(i omega +s)t) \ dt`

`= - (1)/(i omega + s) [ e^(-(i omega +s)t)]_0^(oo)`

`= (1)/(i omega + s) = (s - i omega)/(s^2 + omega ^2)`

`implies mathbb L {cos omega t } = \mathcal (Re) (mathbb L {cos omega t color(red)(-) i sin omega t } )= (s )/(s^2 + omega ^2)`

AND

`implies mathbb L {sin omega t } = -\mathcal (Im) (mathbb L {cos omega t color(red)(-) i sin omega t } )= (omega )/(s^2 + omega ^2)`

Repeat for: `omega = 4`